In a practical triangular-wave generator built with op-amps, which block must follow an op-amp comparator so that the comparator’s two-level output is converted into a linear ramp (triangular) waveform?

Introduction:
A common way to generate a triangular wave in analog electronics is to use a fast switching stage that produces a two-level output, and then a block that converts those levels into a linear ramp. This question checks whether you know the classic comparator-plus-integrator topology used in many waveform generators and function generators.

Given Data / Assumptions:

• The first stage is an op-amp comparator (often with hysteresis like a Schmitt trigger) producing a symmetrical high/low output.
• The second stage should transform a constant high or low level into a steadily changing voltage.
• Idealized op-amp behavior for conceptual understanding.

Concept / Approach:
An integrator outputs the time integral of its input. When the comparator output is at a fixed positive level, the integrator output changes linearly with negative or positive slope depending on polarity. When the comparator flips to the opposite level, the slope reverses. Cascading them yields a continuous up-down ramp, i.e., a triangular wave.

Step-by-Step Solution:
Use a comparator to produce a two-state (±V) signal as the control input.Feed that signal into an op-amp integrator with a resistor at the input and a capacitor in the feedback path.For a constant input ±V, the integrator output changes at a constant rate dv_o/dt = ±V/(R*C).The output ramps until a threshold in the comparator is reached; the comparator toggles and the slope reverses.The repeating reversal generates a triangular waveform at the integrator output.

Verification / Alternative check:
From i = C * dv/dt and i = (V_in − V_node)/R for an inverting integrator, a constant V_in produces a constant dv/dt, ensuring linear ramps. Practical circuits add hysteresis in the comparator to set the amplitude and frequency via R, C, and thresholds.

Why Other Options Are Wrong:

• Differentiator: Produces spikes from edges, not ramps from levels.
• Amplifier: Only scales amplitude; does not create time integration.
• Multivibrator: A general oscillator class; in this chain, the necessary function is integration.
• Schmitt trigger: Often part of the comparator stage, not the ramp-forming stage.

Common Pitfalls:

• Confusing differentiators and integrators because both use RC networks with op-amps.
• Omitting hysteresis in the comparator, which can cause jitter or non-oscillation.
• Ignoring slew-rate and saturation limits that distort the triangular waveform at high frequencies.

Final Answer:
integrator